This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for
applying convolutional neural networks to point clouds. The framework consists of two …

Riemannian geometry has today become a vast and important subject. This new book of
Marcel Berger sets out to introduce readers to most of the living topics of the field and …

Both classical geometry and modern differential geometry have been active subjects of
research throughout the 20th century and lie at the heart of many recent advances in …

Le 28 août 1878,a l'occasion de la septieme réuniona Paris de l'Association pour
l'Avancement de la Science, PL Tchebychev fit une conférence portant le même titre que cet …

We are concerned with the global weak rigidity of the Gauss–Codazzi–Ricci (GCR)
equations on Riemannian manifolds and the corresponding isometric immersions of …

It is known that the SU (2) degrees of freedom manifest in the description of the gravitational
field in loop quantum gravity are generally reduced to U (1) degrees of freedom on an S 2 …

The local adaptive Galerkin bases for large-dimensional dynamical systems, whose long-
time behavior is confined to a finite-dimensional manifold, are optimal bases chosen by a …

This paper focuses on RCD (0, 2)-spaces, which can be thought of as possibly non-smooth
metric measure spaces with non-negative Ricci curvature and dimension less than 2. First …

The local adaptive Galerkin bases for large dynamical systems, whose long time behaviour
is confined to a finite dimensional manifold, are bases chosen by a local version of a …

We prove that a smooth compact submanifold of codimension 2 immersed in R n, n≥ 3,
bounds at most finitely many topologically distinct, compact, nonnegatively curved …